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Precalculus · Unit 1: Core analysis of polynomial and rational function families · 5 min read · Updated 2026-05-11

Polynomial and Rational Functions — AP Precalculus

AP Precalculus · Unit 1: Core analysis of polynomial and rational function families · 5 min read

1. Unit at a Glance

This unit builds from foundational function concepts to full, rigorous analysis of polynomial and rational functions, the two most widely used function families in precalculus and calculus. We start with core concepts of how functions change, then move to algebraic manipulation, polynomial analysis, rational function analysis, modeling, and transformations.

The topic sequence connects algebraic manipulation to graphical interpretation and real-world application, helping you link what you see on a graph to what you can compute algebraically — an essential skill for success on the AP exam.

Common Pitfalls

Why: Many students treat all discontinuities as identical, regardless of whether they are removable

Why: Students often mix up the rules for horizontal asymptotes based on degree comparisons

Why: Students often miss that the conjugate root rule only applies to polynomials with real coefficients

Quick Reference Cheatsheet

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